A273776 Smallest composite number with n distinct prime factors with property that the concatenation of its distinct prime factors, in descending order, is a palindrome.

4, 46, 138, 690, 197890, 5444670, 156719940, 4941906970, 135969743910

Offset: 1

Author

Paolo P. Lava, Jul 06 2016

Keywords

• nonn
• base
• more

Comments

4 = 2 * 2

46 = 2 * 23

138 = 2 * 3 * 23

690 = 2 * 3 * 5 * 23

197890 = 2 * 5 * 7 * 11 * 257

5444670 = 2 * 3 * 5 * 7 * 11 * 2357

156719940 = 2 * 2 * 3 * 5 * 13 * 17 * 53 * 223

4941906970 = 2 * 5 * 7 * 11 * 13 * 17 * 113 * 257

135969743910 = 2 * 3 * 5 * 7 * 11 * 13 * 17 * 113 * 2357

Examples

			Prime factors of 4 are 2, 2 and concat(2,2) = 22 is palindromic.
Prime factors of 46 are 2, 23 and concat(23,2) = 232 is palindromic.
Prime factors of 5444670 are 2, 3, 5, 7, 11, 2357 and concat(2357,11,7,5,3,2) = 2357117532 is palindromic.
		

Crossrefs

Cf. A046449.

Programs

Maple

with(numtheory): T:=proc(w) local x, y, z; x:=0; y:=w; for z from 1 to ilog10(w)+1 do x:=10*x+(y mod 10); y:=trunc(y/10); od; x; end;
P:=proc(q) local a,b,c,i,j,k,n; c:=1; for j from 1 to q do for n from c to q do
if not isprime(n) then a:=ifactors(n)[2]; b:=[]; if nops(a)=j then for k from 1 to nops(a) do
for i from 1 to a[k][2] do b:=[op(b),a[k][1]]; od; od; b:=sort(b); a:=b[nops(b)];
for k from nops(b)-1 by -1 to 1 do a:=a*10^(ilog10(b[k])+1)+b[k]; od;
if T(a)=a then c:=n; print(n); break; fi; fi; fi; od; od; end: P(10^9);

Extensions

a(7)-a(9) from Giovanni Resta